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Polynomial Differential Systems in $$\mathbb {R}^3$$ R 3 Having Invariant Weighted Homogeneous Surfaces

Polynomial Differential Systems in $$\mathbb {R}^3$$ R 3 Having Invariant Weighted Homogeneous... In this paper we give the normal form of all polynomial differential systems in $$\mathbb {R}^3$$ R 3 having a weighted homogeneous surface $$f=0$$ f = 0 as an invariant algebraic surface and characterize among these systems those having a Darboux invariant constructed uniquely using this invariant surface. Using the obtained results we give some examples of stratified vector fields, when $$f=0$$ f = 0 is a singular surface. We also apply the obtained results to study the Vallis system, which is related to the so-called El Niño atmospheric phenomenon, when it has a cone as an invariant algebraic surface, performing a dynamical analysis of the flow of this system restricted to the invariant cone and providing a stratification for this singular surface. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

Polynomial Differential Systems in $$\mathbb {R}^3$$ R 3 Having Invariant Weighted Homogeneous Surfaces

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References (37)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-017-0045-9
Publisher site
See Article on Publisher Site

Abstract

In this paper we give the normal form of all polynomial differential systems in $$\mathbb {R}^3$$ R 3 having a weighted homogeneous surface $$f=0$$ f = 0 as an invariant algebraic surface and characterize among these systems those having a Darboux invariant constructed uniquely using this invariant surface. Using the obtained results we give some examples of stratified vector fields, when $$f=0$$ f = 0 is a singular surface. We also apply the obtained results to study the Vallis system, which is related to the so-called El Niño atmospheric phenomenon, when it has a cone as an invariant algebraic surface, performing a dynamical analysis of the flow of this system restricted to the invariant cone and providing a stratification for this singular surface.

Journal

Bulletin of the Brazilian Mathematical Society, New SeriesSpringer Journals

Published: Jun 27, 2017

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